2826
Energy & Fuels 2008, 22, 2826–2839
Comprehensive Study of Biomass Particle Combustion
Hong Lu,* Warren Robert, Gregory Peirce, Bryan Ripa, and Larry L. Baxter
Chemical Engineering Department, Brigham Yong UniVersity, ProVo, Utah 84602
ReceiVed January 5, 2008. ReVised Manuscript ReceiVed March 13, 2008
This investigation provides a comprehensive analysis of entrained-flow biomass particle combustion processes.
A single-particle reactor provided drying, pyrolysis, and reaction rate data from poplar particle samples with
sizes ranging from 3 to 15 mm. A one-dimensional particle model simulates the drying, rapid pyrolysis,
gasification, and char oxidation processes of particles with different shapes. The model characterizes particles
in three basic shapes (sphere, cylinder, and flat plate). With the particle geometric information (particle aspect
ratio, volume, and surface area) included, this model can be modified to simulate the combustion process of
biomass particles of any shape. The model also predicts the surrounding flame combustion behaviors of a
single particle. Model simulations of the three shapes agree nearly within experimental uncertainty with the
data. Investigations show that spherical mathematical approximations for fuels that either originate in or form
aspherical shapes during combustion poorly represent combustion behavior when particle size exceeds a few
hundred microns. This includes a large fraction of the particles in both biomass and black liquor combustion.
In particular, composition and temperature gradients in particles strongly influence the predicted and measured
rates of temperature rise and combustion, with large particles reacting more slowly than is predicted from
isothermal models.
1. Introduction
During the past two decades, interest in renewable energy
sources has increased due to at least two driving forces: (1) the
increasing concern about the environmental impact of fossil and
nuclear energy; and (2) the increasing anxiety regarding the
security and longevity of fossil fuel.
The threat of regional and global climate change (global
warming) may require significant reduction in the emissions of
greenhouse gasessmost notably CO2. One potential strategy
for reducing such emissions is the replacement of fossil fuels
with renewable biomass fuels. Renewable fuels can be essentially CO2-neutral if derived from sustainable cultivation
practices with minimal fossil fuel usage. Unlike fossil fuels,
biomass fuels can be renewable and CO2-neutral in the sense
that the CO2 generated by biomass utilization recycles from the
atmosphere to the plants that replace the fuel, closing the carbon
loop on a short time scale. If the biomass is renewably produced
(as is generally the case in developed nations), there is little
net increase in atmospheric CO2 content. Since most biomass,
including essentially all biomass residue, decays in any case,
sometimes producing methane and other decomposition products
that greatly exceed the potency of CO2 as greenhouse gases,
use of biomass residues as fuel has the potential of actually
decreasing greenhouse gas impacts, not just being neutral.1
Di Blasi2 investigated the influences of physical properties
on biomass devolatilization. A detailed particle energy and mass
transport model predicted the effects of density, thermal
conductivity, permeability to gas flow, and specific heat capacity.
* To whom correspondence should be addressed. Telephone: 1-949-3308970. Fax: 1-949-330-8994. E-mail: [email protected]. Current
address: 18A Mason, Irvine, CA 92618.
(1) Mann, M. A Comparison of the Environmental Consequences of
Power from Biomass, Coal, and Natural Gas; 2001. (cited; available from
http://www.nrel.gov/analysis/pdfs/2001/novdc.pdf.
(2) Di Blasi, C. Influences of Physical Properties on Biomass Devolatilization Characteristics. Fuel 1997, 76, 957–964.
The author concluded that variations in physical properties
mainly affect reactivities of secondary reactions of tar vapors
and the conversion time for conversion in a thermally thick
regime (intraparticle heat transfer control). Biomass density and
the char thermal conductivity exhibit the highest sensitivity.
Miller and Bellan3 performed a parametric investigation of
reactor temperature, heating rate, porosity, initial particle size,
and initial temperature effects on char yields and conversion
times using a spherically symmetric particle pyrolysis model.
An increase in heating rate decreased both the char yield and
the conversion time for both cellulose and wood. Additionally,
both char yield and conversion time are increasing functions of
initial particle size.3 The char yield increase arises from
secondary reactions between tar vapor and solids in the particle
and the lower temperature heat-up.
Baxter and Robinson4 applied engineering models of kinetics,
heat transfer, and mass transfer to predict the effects of particle
size and density, shape, internal temperature gradients, and
composition. The results of mass loss history of biomass
particles were compared with data collected from several highly
instrumented furnaces. Drying and devolatilization were found
to be primarily heat-transfer controlled whereas oxidation was
found to be primarily mass-transfer controlled for most biomass
of practical concern. In their later research, they found devolatilization removes most of the mass. Under rapid, hightemperature pyrolysis conditions, up to 95 wt % (daf) of the
mass is released during devolatilization, significantly more than
ASTM tests.
The effects of particle size, reactor heating rate, and final
reactor temperature were theoretically and experimentally
(3) Miller, R. S.; Bellan, J. Analysis of Reaction Products and Conversion
Time in the Pyrolysis of Cellulose and Wood Particles. Combust. Sci.
Technol. 1996, 119, 331–373.
(4) Bharadwaj, A.; Baxter, L. L.; Robinson, A. L. Effects of intraparticle
heat and mass transfer on biomass devolatilization: Experimental results
and model predictions. Energy Fuels 2004, 18, 1021–1031.
10.1021/ef800006z CCC: $40.75  2008 American Chemical Society
Published on Web 05/15/2008
Biomass Particle Combustion
investigated by Di Blasi.5 Similar results were obtained: large
particle size increases char yields; higher heating rates result in
higher volatile yields and lower char yields. This researech
indicates three main regimes of solid-fuel pyrolysis: the
thermally thick (diameter ) 0.625 cm), the thermally thin
(diameter ) 0.04 cm), and the pure kinetic regime. The pure
kinetic limit involves only particles at least 1 order of magnitude
smaller than those allowing conversion in the thermally thin
regime, except at very low temperatures.
As for particle shape, a spherical particle shape is usually
assumed in modeling work for convenience. Other particle
shapes have been considered. Jalan and Srivastava6 studied
pyrolysis of a single cylindrical biomass particle, and particle
size and heating rate effects were investigated. In Horbaj’s
model7 and Liliddahl’s model,8 a particle geometric factor was
introduced to account for the particle shape, which can deal
with a prism (or slab), a cylinder (or rod), and a sphere.
In 2000, Janse and Westerhout9 simulated the flash pyrolysis
of a single wood particle. To investigate the influence of particle
shape, simulations included spherical, cylindrical, and flat
particles. Results show that spherical particles react most quickly
compared to other particle shapes if the characteristic size is
taken as the minimum particle dimension. The higher surfacearea-to-volume ratio of spherical particles on this basis explains
this observation; flat particles react most slowly. In the work
reported later in this document, the characteristic dimension is
taken as the spherical-equivalent diameter: the diameter of a
sphere with the same volume/mass as the aspherical particle.
As will be shown, using the spherical-equivalent diameter results
in the opposite trendsspherical particles react most slowly.
There is no inconsistency in these results, just a difference in
basis of comparison. At small particle diameters (typically less
than 200 µm), the rate of reaction becomes dominant and the
different particle shapes exhibit nearly equal conversion times.
Flat particles seem to yield less gas and more char. This research
also showed that an increase in particle diameter (or conversion
time) caused no change in bio-oil yield, a slight decrease in
gas yield, and a slight increase in char yield. This might be due
to the low reactor temperature (surface temperature 823 K) they
used to simulate this process.
Coal char reactivity and oxidation processes enjoy an
extensive literature developed during the last decades. Char,
either from coal or biomass, is usually considered to be mainly
composed of carbon, containing far fewer heteroatoms (O, H,
S, and N) than the fuels from which they derive but nonetheless
retaining some heteroatoms and in any case having structures
and reactivity very different from graphite. In this sense, the
chemical structure of biomass char is similar to coal char, but
large physical differences exist between them, such as density,
thermal conductivity, porosity, surface area, and particle shape
and size.
(5) Di Blasi, C. Kinetics and Heat Transfer Control in the Slow and
Flash Pyrolysis of Solids. Ind. Eng. Chem. Res. 1996, 35, 37–46.
(6) Jalan, R. K.; Srivastava, V. K. Studies on Pyrolysis of a Single
Biomass Cylindrical Pellet Kinetic and Heat Transfer Effects. Energy
ConVers. Manage. 1999, 40 (5), 467–494.
(7) Horbaj, P. Model of the Kinetics of Biomass Pyrolysis. DreVarsky
Vyskum 1997, 42 (4), 15–23.
(8) Liliedahl, T.; Sjostrom, K. Heat transfer controlled pyrolysis kinetics
of a biomass slab, rod or sphere. Biomass Bioenergy 1998, 15 (6), 503–
509.
(9) Janse, A. M. C.; Westerhout, R. W. J.; Prins, W. Modelling of Flash
Pyrolysis of a Single Wood Particle. Chem. Eng. Process. 2000, 39, 239–
252.
Energy & Fuels, Vol. 22, No. 4, 2008 2827
Mermoud and his co-workers10 collected experimental steam
gasification reactivity data with beech char and compared with
model predictions. The usual homogeneous or shrinking core
particle models produced unacceptable results and that only the
assumption of thermal equilibrium between the particle and the
surrounding gas is valid for a model at bed scale.
With birch wood chars obtained from a free-fall tubular
reactor and a thermobalance, Chen et al.11 studied char reactivity
with carbon dioxide and steam in the thermobalance. Reaction
rates of the char depend strongly on particle temperature history
during char formation. Chars obtained from rapid pyrolysis
possessed higher reactivity (2.3-2.4 times higher) in the reaction
with carbon dioxide or steam compared with chars from slow
pyrolysis. In other words, kinetic rates of char increase with
increasing particle heating rate during the thermal decomposition
process.
The reactivity of two kinds of biomass chars from Southern
pine and switchgrass was investigated by Wornat et al.12 Results
showed that, at early stages of char conversion, both of the chars
were quite reactive. However, their reactivity decreased somewhat during char conversion as more reactive carbon is
preferentially depleted and the inorganic constituents of the chars
underwent physical and chemical transformations that render
them less catalytically active. They also found that even with
small biomass char particles (75-106 µm), the irregular
morphologies and their wide range of burning rates made a more
rigorous and detailed kinetic analysis quite difficult.
Results from Di Blasi and co-workers13 indicate that in the
kinetically controlled regime (low temperature ∼873 K) and
under nonisothermal conditions (10, 20-80 K/min heating rate),
the reactivities (dm/dt) of three biomass chars (wheat straw, olive
husks, and grape residues) increased with conversion first,
reaching a maximum, and decreased or remained constant, then
increased again as a function of conversion. A one-step global
model interprets the mass loss curves in their work with
conversion-dependent parameters. At low temperatures in a
TGA, Adanez and his co-workers14 determined combustion
reactivities of five biomass chars with a combined method, with
similar results.
A recent paper15 investigated the combustion characteristics
of moving and suspended biomass particles both experimentally
and mathematically. It was found that isothermal particle
assumption is no longer valid when particle size exceeds
150-200 µm.
Detailed single biomass particle combustion data, including
particle mass loss and temperature history as functions of time,
is rarely reported in the above literature. This investigation
summarizes experimental drying, devolatilization conversion,
and char oxidation rates for poplar particles in a single particle
reactor, as well as a model that predicts these data nearly within
(10) Mermoud, F.; Golfier, F.; Salvador, S.; Van de Steene, L.; Dirion,
J. L. Experimental and numerical study of steam gasification of a single
charcoal particle. Combust. Flame 2006, 145, 59–79.
(11) Chen, G.; Yu, Q.; Sjostrom, K. Reactivity of Char from Pyrolysis
of Birch Wood. J. Anal. Appl. Pyrolysis 1997, 40-41, 491–499.
(12) Wornat, M. J., Hurt, R. H.; Davis, K. A.; Yang, N. Y. C. SingleParticle Combustion of Two Biomass Chars. In Twenty-Sixth Symposium
(International) on Combustion; The Combustion Institute: Pittsburgh, PA,
1999.
(13) Di Blasi, C.; Buonanno, F.; Branca, C. Reactivities of Some
Biomass Chars in Air. Carbon 1999, 37, 1227–1238.
(14) Adanez, J.; de Diego, L. F.; Garcia-Labiano, F.; Abad, A.;
Abanades, J. C. Determination of Biomass Char Combustion Reactivities
for FBC Applications by a Combined Method. Ind. Eng. Chem. Res. 2001,
40, 4317–4323.
(15) Yang, Y. B.; Sharifi, V. N.; Swithenbank, J.; Ma, L.; Darvell, L. I.;
Jones, J. M.; Pourkashanian, M.; Williams, A. Combustion of a Single
Particle of Biomass. Energy Fuels 2008, 22, 306–316.
2828 Energy & Fuels, Vol. 22, No. 4, 2008
Lu et al.
Figure 2. Moisture drying scheme.
Figure 1. Single-particle reactor schematic diagram.
their experimental uncertainty, providing detailed descriptions
of particle mass and temperature change for a single particle
during combustion.
2. Experimental Method
A single-particle reactor16 is used to investigate the drying,
devolatilization, and char oxidation/gasification behaviors of biomass particles. Figure 1 schematically illustrates the experimental
facility for the single particle combustion study.
Poplar particles with two regular shapes, cylinder and nearsphere, were obtained by cutting 9.5 mm diameter poplar dowel
rod to different aspect ratios: 1.0 for near-spherical and 4.0 for
cylindrical particles. Moisture content of the samples is usually
about 6%. To study the drying behavior of biomass particles,
samples with higher moisture contents were also prepared by
soaking in water for different periods and kept in closed sample
bottles.
Single biomass particles suspended on a type B or type K
thermocouple and connected to a wireless data logger, from PACE
Scientific, provided internal temperature data at a speed of 20 Hz.
The data logger, thermocouple, and the biomass particle were placed
on top of a balance to provide dynamic mass loss data. A small
hole of about the same size of the thermal couple wire (∼0.25 mm)
was drilled through the center the particle for thermocouple
suspension. Mass loss data were collected and recorded with the
balance with a resolution of 0.1 mg. The imaging system and optical
pyrometer recorded the physical changes and surface temperature
distribution of the biomass particle. The data logger, balance, and
imaging system collect data simultaneously. All equipment and
devices are synchronized within 1 s. For particle devolatilization
processes, particle surface temperature was also measured by a
thermocouple. To reduce the influence of thermal conduction on
surface temperature measurement, a shallow and narrow groove
was cut on the particle surface and the wire was buried next to the
surface.
This single-particle reactor produces experimental data, including
mass loss, and surface and center temperature, as functions of time
for poplar dowel particles during drying, pyrolysis, and char
oxidation/gasification processes.
3. Particle Mathematical Model
As a biomass particle hovers in the single-particle reactor
with air as carrier gas, it exchanges energy by both radiation
and convection and by chemical reactions. The biomass particle
undergoes the following processes: drying, devolatilization,
volatiles combustion, char gasification, and char oxidation. These
(16) Ip, L.-T. Comprehensive black liquor droplet combustion studies.
Chemical Engineering; Brigham Young University: Provo, UT, 2005.
processes may occur sequentially or simultaneously, depending
on particle properties and reactor conditions.
Mechanisms of Drying, Devolatilization, and Char
Gasification and Oxidation. Moisture in biomass occurs in two
forms: free water and bound water.17 Moisture content above
the fiber saturation point (FSP) is free water, that is, exists in
liquid form in pores and cells. Below the FSP, moisture is bound
water, that is, exists as moisture physically or chemically bound
to surface sites or as hydrated species. The average FSP is about
30%,17 which is the weight of water in the wood as a percentage
of the weight of oven-dry wood (essentially water content on a
dry basis). Traditionally, the forest products industries express
moisture on this basis, so that 100% moisture means essentially
half of the mass is water. Nuclear magnetic resonance (NMR)
can determine free water and bound water contents.18 Free
moisture vaporizes from both the internal and external surface
at a rate determined by the surface saturated vapor pressure,
the partial pressure of vapor in the gas phase. Bound water does
not vaporize in a manner similar to free moisture but rather is
released as a result of chemical reactions releasing bound
hydrates and similar processes. Four basic methods, including
a thermal model, equilibrium model, and chemical reaction
model, describe wood drying under combustion heat fluxes.19
In this model, a mass transfer expression, with the difference
between equilibrium vapor pressure and vapor partial pressure
as the driving force, describes both the evaporation of free water
and recondensation of vapor. The evaporation rate of bound
water proceeds by a chemical reaction rate expression.20 Figure
2 illustrates the drying scheme of moisture. Poplar particles used
in the single-particle reactor usually have 6% moisture content,
which is categorized as bound water. Samples with higher
moisture content, up to 50%, were also prepared and used to
collect free-water drying process data and validate the drying
model.
Devolatilization or pyrolysis involves heating of raw biomass
components or organic materials in the absence of oxidizer,
thermal degradation of the biomass components, mass transport
of the devolatilization products by advection and diffusion, and
escape of products at the surface of the particle. A few authors
distinguish between pyrolysis and devolatilization, with the
former occurring in a neutral or reducing environment and the
latter in an oxidizing environment. Most particles thermally
decompose within a volatile cloud (reducing environment) even
(17) Forest Products Laboratory United States Department of Agriculture
Forest Service. Physical Properties and Moisture Relations of Wood. In
Wood Handbook: Wood as an Engineering Material; Forest Products
Society: Madison, WI, 1999; Chapter 3, pp 3-5.
(18) Guzenda, R.; Olek, W. Identification of free and bound water
content in wood by means of NMR relaxometry. In 12th International
Symposium on NondestructiVe Testing of Wood; Sopron: Budapest, Hungary,
2000.
(19) Bryden, K. M.; Hagge, M. J. Modeling the combined impact of
moisture and char shrinkage on the pyrolysis of a biomass particle. Fuel
2003, 82, 1633–1644.
(20) Chan, W.-C.R.; Kelbon, M.; Krieger, B. B. Modeling and experimental verification of physical and chemical processes during pyrolysis of
a large biomass particle. Fuel 1985, 64 (11), 1505–1513.
Biomass Particle Combustion
Energy & Fuels, Vol. 22, No. 4, 2008 2829
Figure 3. Two-stage wood pyrolysis model.21
Table 1. Light Gas Composition Produced during
Devolatilization
components
H2
CO
CO2
H2O
light hydrocarbon
mass fraction
0.109
0.396
0.209
0.249
0.127
when the overall environment is oxidizing, making this distinction somewhat ambiguous. The two terms are used interchangeably in this document, consistent with most of the literature.
The two-stage wood pyrolysis kinetics model, shown in Figure
3, is chosen for this particle model since it is capable of
predicting the product yields and distribution variations with
temperature and heating rate which are significantly influenced
by particle shape and size.
The volatile yield from pyrolysis includes a complex mixture
and more than 100 hydrocarbons were found.22–24 Pyrolysis
product distribution depends strongly on reactor temperature,
heating rate, residence time, and mass transfer velocity and
pressure.24 This complex mixture mainly consists of CO, CO2,
H2O, H2, light hydrocarbons, and heavy hydrocarbons. The first
five components are classified as light gas, and the last one as
tar. For the light gas composition, reaction kinetics from
Thunman et. al25 predict wood pyrolysis volatile components
in this model, with the mass fraction of each species listed in
Table 1. To simplify the combustion behaviors of volatiles, the
light hydrocarbon and heavy hydrocarbon are lumped together
as hydrocarbons in the current investigation, and the lumped
hydrocarbon molecule is C6H6.2O0.2, consistent with published
results.25 In this model, hydrocarbon combustion in the gas phase
occurs through a one-step global reaction according to the
approximate composition of hydrocarbon, even though the
combustion chemistry of a simple gas could be a complex
phenomenon.26 The reaction mechanism and kinetic parameters
for the hydrocarbon combustion are based on the recommendations of Smoot and Smith.27
Char gasification and oxidation include five classic heterogeneous and homogeneous reactions, indicated as reactions
8-12 in Table 2. In coal char combustion, reaction 8 is
(21) Di Blasi, C. Heat, Momentum and Mass Transport through a
Shrinking Biomass Particle Exposed to Thermal Radiation. Chem. Eng. Sci.
1996, 51 (7), 1121–1132.
(22) Evans, R. J.; Milne, T. A. Molecular Characterization of the
Pyrolysis of Biomass. 1. Fundamentals. Energy Fuels 1987, 1, 123–137.
(23) Evans, R. J.; Milne, T. A. Molecular Characterization of the
Pyrolysis of Biomass. 2. Applications. Energy Fuels 1987, 1, 311–319.
(24) Demyirbas, A. Hydrocarbons from Pyrolysis and Hydrolysis
Processes of Biomass. Energy Sources 2003, 25, 67–75.
(25) Thunman, H.; Niklasson, F.; Johnsson, F.; Leckner, B. Composition
of Volatile Gases and Thermochemical Properties of Wood for Modeling
of Fixed or Fluidized Beds. Energy Fuels 2001, 15, 1488–1497.
(26) Warnatz, J. Hydrocarbon oxidation high-temperature chemistry.
Pure Appl. Chem. 2000, 72 (11), 2101–2110.
(27) Smoot, L. D.; Smith, P. J. Coal Combustion and Gasification;
Plenum Press: New York, 1985.
described by both first- and half-order expressions.28,29 Biomass
char reactivity literature is less substantial than that for coal
char, but some report that biomass char has slightly higher
reactivity than that of coal.12,13,30,31 The oxidation rate of biomass
char varies between a half- and first-order, as demonstrated by
Janse et al.32 According to Bryden’s33 analysis, lignite’s kinetic
parameters are used for wood char oxidation since wood char
more closely resembles lignite than other coal types. The
oxidation kinetic mechanisms make this model more robust,
but in practice oxidation occurs mostly under diffusioncontrolled conditions, in which case the details of the kinetics
are immaterial.
Parameters describing chemical reactions and phase changes,
together with their corresponding rate expressions during drying,
devolatilization, and char oxidation processes, appear in
Table 2.
Arrhenius expressions describe the temperature dependence
of the kinetic rate coefficients for reactions 1-5 and 7-13, as
indicated in eqs 1 and 2.
In reactions 1-5, 7, and 11-13
Ei
(1)
ki ) Ai exp RT
and in reactions 8-10,
Ei
ki ) AiT exp (2)
RT
The literature-based kinetic parameters for wood pyrolysis
vary widely. They are usually measured at low to moderate
temperature (usually <900 K). No high-temperature kinetic data
for the two-stage scheme appear in the literature. Font et al.35
presented kinetic data for the three primary reactions that are
found to be comparable to what Nunn et al.36 reported for the
single reaction kinetic data for hardwood in the high-temperature
range (573-1373 K). Font et al.’s results are used in this model
for sawdust samples, and Wagenaar’s37 pine wood pyrolysis
kinetics data are applied for poplar samples. The pre-exponential
factors, activation energy, and standard heats of reaction for all
the reactions used in this model appear in Table 3.
Heat, Mass, and Momentum Transfer Control Equations. The following assumptions allow tractable mathematical
combustion model development:
( )
( )
(28) Smith, K. L.; Smoot, L. D.; Fletcher, T. H.; Pugmire, R. J. The
structure and reaction processes of coal. In The Plenum Chemical Engineering Series; Luss, D., Ed.; Plenum Press: New York, 1994.
(29) Brewster, B. S.; Hill, S. C.; Radulovic, P. T.; Smoot, L. D.
Fundamentals of Coal Combustion for Clean and Efficient Use; Smoot,
L. D. , Ed.; Elsevier Applied Science Publishers: London, 1993; Vol. 20.
(30) Blackham, A. U.; Smoot, L. D.; Yousefi, P. Rates of oxidation of
millimetre-sized char particles: simple experiments. Fuel 1994, 73 (4), 602–
612.
(31) Evans, D. H.; Emmons, H. W. Combustion of wood charcoal. Fire
Res. 1977, (1), 57–66.
(32) Janse, A. M. C.; de Jonge, H. G.; Prins, W.; van Swaaij, W. P. M.
Combustion kinetics of char obtained by flash pyrolysis of pine wood. Ind.
Eng. Chem. Res. 1998, 37, 3909–3918.
(33) Bryden, K. M. Computational Modeling of Wood Combustion;
Mechanical Engineering Department, University of Wisconsin-Madison:
Madison, WI, 1998.
(34) Hautman, D. J.; Dryer, L.; Schug, K. P.; Glassman, I. A multiplestep overall kinetic mechanism for the oxidation of hydrocarbons. Combust.
Sci. Technol. 1981, 25, 219–235.
(35) Font, F.; Marcilla, A.; Verdu, E.; Devesa, J. Kinetics of the pyrolysis
of almond shells and almond shells impregnated with CoCl2 in a fluidized
bed reactor and in a pyroprobe 100. Ind. Eng. Chem. Res. 1990, 29, 1846–
1855.
(36) Nunn, T. R.; Howard, J. P.; Longwell, T.; Peters, W.A. Product
compositions and kinetics in the rapid pyrolysis of sweet gum hardwood.
Ind. Eng. Chem., Process Des. DeV. 1985, 24, 836–844.
(37) Wagenaar, B. M.; Prins, W.; Van Swaaij, W. P. Flash pyrolysis
kinetics of pine wood. Fuel Process. Technol. 1993, 36, 291.
2830 Energy & Fuels, Vol. 22, No. 4, 2008
Lu et al.
Table 2. Chemical Reactions, Phase Change and Rate Expressions
reaction index
reaction description
rate expression
ref
1
2
3
4
5
6
7
8
9
10
11
12
13
biomass f light gas
biomass f tar
biomass f char
tar f light gas
tar f char
H2O(l,free) T H2O(g)
H2O(l,bound) f H2O(g)
C + 1/2O2 f CO
C + CO2 f 2CO
C + H2O f CO + H2
1/ O + CO f CO
2 2
2
H2 + 1/2O2 f H2O
C6H6.2O0.2 + 2.9O2 f 6CO + 3.1H2
r1 ) ∂FB/∂t ) k1FB
r2 ) ∂FB/∂t ) k2FB
r3 ) ∂FB/∂t ) k3FB
r4 ) ∂FG/∂t ) εk4FgYT
r5 ) ∂FC/∂t ) εk5FgYT
0 )h
sat
r6 ) ∂Ffw/∂t ) sa(Ffw/Ffw
m,pore(FV - YVFg)
r7 ) ∂Fbw/∂t ) k7Fbw
r8 ) ∂CO2/∂t ) sa,char[FC/(FC + FB + FA)]k8εCO2
r9 ) ∂CCO2/∂t ) sa,char[FC/(FC + FB + FA)]k9εCCO2
r10 ) ∂CH2O/∂t ) sa,char[FC/(FC + FB + FA)]k10εCH2O
r11 ) ∂CCO/∂t ) k11CCOCO20.25CH2O0.5
r12 ) ∂CH2/∂t ) k12CH2CO21.42
r13 ) ∂CHC/∂t ) k13CHC0.5CO2
20
31
29
29
34
34
27
Table 3. Kinetic Data and Heats of Reaction
a
reaction index
A (1/s)
E (kJ/mol)
ref
temp range (K)
1 (hardwood sawdust)a
1 (poplar)a
2 (hardwood sawdust)a
2 (poplar)a
3 (hardwood sawdust)a
3 (poplar)a
4
5
6
8
9
10
11
12
13
1.52 × 107
1.11 × 1011
5.85 × 106
9.28 × 109
2.98 × 103
3.05 × 107
4.28 × 106
1.0 × 105
5.13 × 1010
0.658 (m/(s · K))
3.42 (m/(s · K))
3.42 (m/(s · K))
1012.35
1012.71
104.32 × T × 0.3P
139.2
177
119
149
73.1
125
107.5
107.5
88
74.8
130
130
167
171.3
80.2
35
37
35
37
35
37
38
40
19
31
29
29
34
34
27
733-878
573-873
733-878
573-873
733-878
573-873
-
∆H (kJ/kg)
ref
-418
20
-418
20
-418
20
42
42
-2440
9212
14370
10940
10110
120900
41600
39
39
19
19
41
41
41
41
33
These are all one-step kinetics for pyrolysis.
• a transient one-dimensional model sufficiently describes
particle behavior;
• local thermal equilibrium exists between the solid and gas
phase in the particle, so internal temperatures and their gradients
are the same for the solid and gas;
• gases behave as ideal gases, including both relationships
between pressure, temperature, and specific volume and dependence of heat capacity on temperature only;
• particle aspect ratios and shapes do not change during
devolatilization, though size does change dynamically. The
shape and aspect ratio is a simplifying assumption for this case
but not required by the model in general;
• heat and mass transfer at particle boundaries increase relative
to that of a sphere by the ratio of the particle surface to that of
a volume-equivalent spheresa close approximation to results
from more detailed analyses for similarly sized particles.
Particle shapes represented by a parameter n include a sphere
(n ) 2), cylinder (n ) 1), and flat plate (n ) 0). The biomass
particle initially contains inert gas or air. In total, 12 species
appear in the model: biomass, char, free water, bound water,
ash, CO, CO2, H2O, H2, O2, lumped hydrocarbon (tar), and inert
gas. The mass conservation of each species, the momentum,
(38) Liden, C. K.; Berruti, F.; Scott, D. S. A kinetic model for the
production of liquids from the flash pyrolysis of biomass. Chem. Eng.
Commun. 1988, 65, 207–221.
(39) Koufopanos, C. A.; Papayannakos, N.; Maschio, G.; Lucchesi, A.
Modelling of the Pyrolysis of Biomass Particles. Studies on Kinetics,
Thermal and Heat Transfer Effects, Can. J. Chem. Eng. 1991, 69 (4), 907–
915.
(40) Di Blasi, C. Analysis of convection and secondary reaction effects
within porous solid fuels undergoing pyrolysis. Combust. Sci. Technol. 1993,
90, 315–340.
(41) Turns, S. R. An Introduction to Combustion: Concepts and
Applications, 2nd ed.; McGraw-Hill: New York, 2000.
and the total energy equations, as well as the initial and boundary
conditions, appear as eqs 3–33.
The biomass temporal mass balance contains three consumption terms, one each for the reactions to light gas, tar, and char,
where all terms in this expression and most terms in subsequent
expressions depend on both time and position.
∂FB
) SB
∂t
where SB ) - (r1 + r2 + r3)
(3)
Similarly, the char temporal mass balance contains five source
terms, one from the conversion of biomass to char and one for
the char yield from the secondary reactions of tar, as well as
the gasification and oxidation reactions.
∂FC
) SC
∂t
where
SC ) r3 + r5 - r8
2MC
MC
MC
- r9
- r10
MO2
MCO2
MH2O
(4)
The temporal free-water mass balance contains a loss associated with conversion to vapor and a source term associated with
water vapor readsorption into the particle, as determined by
reaction 6 in Table 2. The free water also migrates due to the
pressure gradient in the liquid phase.42,43 The migration flux is
based on Darcy’s law for this porous media, which is propor(42) Ouelhazi, N.; Arnaud, G.; Fohr, J. P. A Two-dimensional study of
wood plank drying. The effect of gaseous pressure below boiling point.
Transp. Porous Media 1992, 7 (1), 39–61.
(43) De Paiva Souza, M. E.; Nebra, S. A. Heat and mass transfer model
in wood chip drying. Wood Fiber Sci. 2000, 32 (2), 153–163.
Biomass Particle Combustion
Energy & Fuels, Vol. 22, No. 4, 2008 2831
tional to the total liquid pressure gradient. The total liquid
pressure is equal to the pressure of the gas phase minus the
capillary pressure of the gas-liquid interface. An effective free
water diffusivity Deff,fwis derived to describe the migration with
Fick’s law applied based on the Darcy’s law results.43 Equation
5 gives the mass balance for free water. The mass transfer
coefficient of vapor in the pore hm,pore, which appears in the
evaporation rate reaction 6, is determined by eq 6.44
(
The overall gas-phase continuity equation results from the sum
of these species and has the form
∂
1 ∂ n
εF +
(r εFgu) ) Sg
∂t g rn ∂r
where
Sg ) r1 + r2 - r5 + r6 + r7 + r8
)
∂Ffw 1 ∂ n
∂Ffw
) n
r Deff,fw
+ Sfw
∂t
∂r
∂r
r
(11)
The gas-phase velocity in the particle obeys a Darcy law type
expression
where
Sfw ) -r6
(5)
hm,pore ) 3.66 × Deff,H2O/dpore_hydraulic
(6)
Bound water has similar migration in the radial direction but
responds to a chemical potential gradient rather than a pressure/
concentration gradient, and the phase change follows the
chemical reaction r7, shown in Equation 7.
(
)
where
η)
Sbw ) -r7
(7)
Several different correlations describe diffusivities of free
water and bound water;42,43,45 Olek et al.’s method is applied
in this investigation. The diffusivities of both free water and
bound water are direction dependent, and the diffusivity in the
axial direction is larger than that in the tangential direction.
Details appear at the end of this section in the physical property
list.
The ash in the particle is assumed to be inert, so that ash
density is constant for nonshrinking/swelling particle
(8)
(
)
∂Yi
∂
∂ n
1 ∂ n
εF Y +
r εDeff,iFg
+ Si (9)
(r εFgYiu) ) 1n ∂r
∂t g i rn ∂r
∂r
r
The conservation equations for all gas-phase components
(CO, CO2, H2O, O2, H2, HC, and inert gas) include temporal
and spatial gradients, convection, and source terms as follows.
Source terms for each gas-phase species appear below:
SCO2 ) r11
r11
r10
MCO2
MCO
- r9 + (r1 + r4)RCO2SCO ) r8
2MCO
2MCO
+ r9
+
MO2
MCO2
MCO
6MCO
+ r13
- r11 + (r1 + r4)RCOSO2 ) -r8 MH2O
MHC
MO2
2MCO
MH2
MH2O
r10 + r12
- r12
MO2
2MH2
- r12 + r13
MH2O
MH2
- r13
3.1MH2
MHC
2.9MO2
MHC
FgRgT
MW
p)
where
∂FA
)0
∂t
η ∂p
µ ∂r
u)-
(12)
The gas mixture is ideal, and the permeability, η, is a massweighted function of the individual solid-phase permeabilities:
∂Fbw 1 ∂ n
∂Fbw
) n
r Deff,bw
+ Sbw
∂t
∂r
∂r
r
r10
2MC
MC
MC
+ r9
+ r9
MO2
MCO2
MH2O
SH2 ) (r1 + r4)RH2 +
SH2O ) (r1 + r4)RH2O + r6 + r7 -
)
(13)
The energy conservation equation includes the following terms:
∂
∂t
[∑
i
FiĤi +
∑ F H + εF ∑ Y Ĥ
ˆ
k
k
[
g
k
j
j
1 ∂ n
r εFgu
rn ∂r
j
]
∑ Y Ĥ ] ) r1
j
[(
j
n
j
1 ∂ n
r Fgε
rn ∂r
∑D
eff,j
j
+
∂ n ∂T
r Keff
+
∂r
∂r
(
)
∂Yj ˆ
∂Fk
H + Deff,k Ĥk
∂r j
∂r
)]
(14)
0 + ∫T C
where Ĥl ) Ĥl,f
T0 p,l (T) dT, l is any species involved, i
) any species or component in the solid phase, j ) any species
or component in the gas phase, and k ) free water and bound
water.
This form of the energy equation relates to standard theoretical analyses46 for multicomponent systems. In eq 14, the first
term represents the energy accumulation, the second term
represents energy convection, the third term (first term after the
equality) accounts for conduction heat transfer, and the last term
accounts for energy associated with species diffusion in the gas
phase and the liquid phase. The last term generally contributes
only negligibly to the overall energy balance and is commonly
justifiably ignored. No heats of reaction appear in the expression
since the energy balances total enthalpy (both phases) and is
not written in terms of temperature or separate particle and gas
phases. Heats of reaction only become apparent when separately
modeling the particle and gas phases or using temperature
instead of enthalpy. Radiation between the gas and solid phase
in the particle is incorporated into the effective conductivity,
as explained below.
The effective diffusivity of gas species in the particle can be
calculated by the parallel pore47 model, as shown in eq 15.
Deff )
SHC ) r2 + (r1 + r4)RHC - r4 - r5 - r13SI ) 0 (10)
(44) Incropera, F. P.; Dewitt, D. P. Fundamentals of Heat and Mass
Transfer, 4th ed.; John Wiley & Sons: New York, 1996.
(45) Olek, W.; Perre, P.; Weres, J. Inverse analysis of the transient bound
water diffusion in wood. Holzforschung 2005, 59 (1), 38–45.
(
FB
FB
ηB + 1 η
FB,0
FB,0 C
Dε
τ
where
(46) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena,
2nd ed.; John Wiley & Sons, Inc.: New York, 2002.
(47) Wheeler, A. AdVances in Catalysis; Academic Press: New York,
1951; p 250.
2832 Energy & Fuels, Vol. 22, No. 4, 2008
Lu et al.
1
1
1
)
+
D DAB DK
(15)
An identical diffusivity for each species and Fickian diffusion
assumptions, as implied here, avoid the complexity of more
formal multicomponent diffusion calculations.
The effective particle thermal conductivity includes radiative
and conductive components with some theoretical basis48,49 and
with empirical verification for wood.9
Keff ) Kcond + Krad
(16)
where the particle structure is assumed to be close to the upper
limit for thermal conductivity; that is, it is assumed to have
high connectivity in the direction of conduction
[
Kcond ) εKgas + (1 - ε)
Kgas )
∑YK
)]
(
FB
FB
K + 1K
FB,0 B
FB,0 C
(17)
j j
j
and where radiation contributes approximately to the third power
of the temperature
εσT3dpore
(18)
Krad )
ω
The emissivity of the particle is the mass-weighted result of
each solid component: biomass, ash, and char. A volumeweighted emissivity might be more appropriate, but it is not
available in this case: all components are assumed to occupy
the same total volume.
ω)
FA
∑F
i
ωA +
FB
∑F
ωB +
i
FC
∑F
ωC
(19)
i
The thermal conductivity of a wet biomass particle is based
on Ouelhazi’s42 empirical correlation which states that the
effective thermal conductivity is a function of temperature and
moisture contents. Thermal conductivity is anisotropic, with the
value in the fiber direction 2.5 times that in the transversal
direction. An average value of both the fiber and transveral
directions is adopted in this paper. Details of the thermal
conductivity of the wet biomass particle appear at the end of
this section.
Initial conditions depend on experimental conditions for a
nonreacting particle. That is, at t ) 0
p(t ) 0, r) ) patm
T(t ) 0, r) ) 300 K (typically)
u(t ) 0, r) ) 0
YI(t ) 0, r) ) 1
Yi(j,k)(t ) 0, r) ) 0
(20)
Boundary conditions at the particle center reflect the spherical
symmetry, that is, at r ) 0
∂p
) 0
∂r t,r ) 0
ut,r ) 0 ) 0
∂T
) 0
∂r t,r ) 0
∂Yi(j,k)
)0
∂r t,r ) 0
(21)
(48) Robinson, A. L.; Buckley, S. G.; Baxter, L. L. Thermal Conductivity
of Ash Deposits 1: Measurement Technique. Energy Fuels 2001, 15, 66–
74.
(49) Robinson, A. L.; Buckley, S. G.; Yang, N. Y. C.; Baxter, L. L.
Thermal Conductivity of Ash Deposits 2: Effects of Sintering. Energy Fuels
2001, 15, 75–84.
During biomass particle combustion, the flame surrounding
the particle may affect particle surface temperature by heat
generated in the flame that feeds back to the surface and further
heats the particle. The model describes both the particle domain
and the boundary layer domain, which includes the flame during
combustion. The boundary layer flame, as with many other
model features, can be turned on or off during simulation.
If the boundary layer domain is off, boundary conditions at
the particle outer surface depend on external conditions of
pressure and heat and mass flux:
p(t, r ) rp) ) patm
∂Yi(j,k)
) θmhmRSA(Yi(j,k),∞ - Yi(j,k),S)
(22)
∂r r ) rp
∂T
4
4
keff r ) rp ) θThTRSA(Tf - T) + RSAωσ(Tw - T )
∂r
where θm and θT represent the blowing factors46 for mass
transfer and heat transfer, respectively. RSA represents the
exterior surface area ratio, which is the surface area of the
particle divided by the characteristic surface area, as follows:
RSA ) SA/(4πRP2) RSA ) SA/(4πRP2AR) RSA ) SA/
(4RP2AR2)
(23)
for spheres, cylinders, and flat plates, respectively.
Each shape employs heat transfer coefficients developed for
that particular shape. Correlations suitable for random particle
orientation during flight appear in the literature for some
particles.50 Where such a model is not available, the characteristic length of the particle is the arithmetic average length of
the particle. For near-spherical particles, Masliyah’s prolate
spheroid model50 provides a suitable correlation, as indicated
in eq 24.
(24)
Nu ) 1.05 + 0.6Re 0.65Pr 0.33
Cylinders at low Reynolds numbers adopt the correlation of
Kurdyumov51 (eq 25).
Nu ) W0(Re)Pr 0.33 + W1(Re)
(25)
The heat transfer coefficient for a flat plate appears in
Equation 26.
(26)
Nu ) 0.644Re 0.5Pr 0.343
Mass transfer coefficient calculations are analogous to heat
transfer correlations respectively for each specific particle shape.
If the boundary layer domain is turned on, the boundary
conditions assume those in the bulk flow (indicated by infinity
subscripts), as shown in eq 27.
pr>)rp ) patm
Yi(j,k)r)rp+BLTm ) Yi(j,k),∞
Tr)rp+BLTT ) T∞
(27)
where BLTm and BLTT are boundary layer thickness of mass
transfer and heat transfer, respectively. The determination of
these two types of boundary layer thicknesses is straightforward
if the particle stays in inert carrier gas (nitrogen). A linear
method is adopted to approximate the boundary layer thicknesses, as illustrated below.
(50) Masliyah, J. H.; Epstein, N. Numerical solution of heat and mass
transfer from spheroids in steady axisymmetric flow. Prog. Heat Mass
Transfer 1972, 6, 613–632.
(51) Kurdyumov, V. N.; Fernandez, E. Heat transfer from a circular
cylinder at low Reynolds numbers. J. Heat Transfer, Trans. ASME 1998,
120 (1), 72–75.
Biomass Particle Combustion
Energy & Fuels, Vol. 22, No. 4, 2008 2833
The linear approximation assumes that the gradient at the
particle surface can be approximated by an algebraic difference:
dY ∆Y Y∞ - YS
≈
)
dr ∆r
BLTm
(28)
The mass transfer at the particle surface is also correlated
with the empirical mass transfer correlation:
DAB
dY
) hmθm(Y∞ - Ys)
dr
(29)
where the mass transfer coefficient can be calculated by
Sh )
dPhm
DAB
(30)
So, substituting eqs 29 and 30 into eq 28 leads to the boundary
layer thickness for mass transfer:
BLTm )
dP
Sh · θm
(31)
Similarly, the boundary layer thickness of heat transfer based
on the linear approximation is
BLTT )
dP
Nu · θT
(32)
When the particle is surrounded by air instead of nitrogen, a
flame forms in the boundary layer. The resulting temperature
and species concentration distributions in the boundary layer
may influence the boundary layer thickness, making it different
from that calculated based on the heat and mass transfer
correlations illustrated above. The determination of the exact
boundary layer thickness for such a burning particle with
surrounding flame could be complicated due to bulk flow
convection (slip velocity) in the reactor axial direction and the
off-gases from the particle. A two-dimensional model might
be needed to predict the exact boundary layer thickness. In this
investigation, eqs 31 and 32 are applied to determine the
thickness of the boundary layer, where flame is formed during
combustion. Model predictions agree well with experimental
data.
To simplify momentum conservation, constant boundary-layer
pressure is assumed, equal to the atmospheric pressure. The
secondary cracking reactions of tar and soot formation in the
boundary layer are neglected, although combustion reactions
are included. A radiation energy flux has to be added to the
energy equation for the node on the particle physical surface
due to the radiation between the particle surface and reactor
wall.
Particle shrinking or swelling during drying, pyrolysis, and
char gasification and oxidation depends on the following
empirical correlation:
V
) 1 + xM(βM - 1.0) + xB(βB - 1.0) + xC(βC - 1.0) (33)
V0
which can be used to describe both shrinking and swelling
behaviors of a burning solid particle or droplet. In eq 33, V is
the current control volume of each cell and V0 initial control
volume of each cell;xm, xB, xC are conversion of moisture,
biomass, and char; βM is the swelling/shrinking factor of
moisture drying, 0.9 for wood particle drying shrinking; βB is
the swelling/shrinking factor of biomass devolatilization, 0.9
for wood particle shrinking; βC is the shrinking factor of char
burning, 0.0 for constant char density shrinking (conceptually
consistent with the typically external diffusion controlled
oxidation rates).
The density change of each species in the solid phase is
determined by the following equation due to volume change.
Fi ∂V
∂Fi
) Si ,
∂t
V ∂t
(34)
where i ) char, ash, and biomass.
The physical properties of the biomass particles significantly
affect the heat and mass transfer rates.2,52 In this work,
temperature-dependent heat capacity correlations are used for
all species. The heat capacity of biomass and char adopt the
model suggested by Merrick.53 Gronli et al.54 suggested a
correlation for tar heat capacity, which is based on some typical
pyrolysis tar components (closely related to benzene). All
physical properties appear in Table 4.
This one-dimensional complete mathematical model for the
combustion of a single biomass particle includes a set of partial
differential equations (PDEs) to describe the mass, heat, and
momentum transfer in the particle domain and the flame layer
domain. A control volume method58 reformulates these differential equations into a set of algebraic equations amenable
to computer simulation. A fully implicit scheme is applied for
the transient term in the energy conservation equation, each
species conservation equation, and momentum equation; the
convection and diffusion/conduction terms are solved by the
power law scheme; control volume faces occur midway between
the grid points; a staggered grid is used for velocity component;
the SIMPLE algorithm is applied for the momentum transfer
to calculate the flow field.
4. Results and Discussion
The single-particle combustion model comparisons with mass
loss data and particle temperature data collected on the singleparticle reactor provide model validation below. Then, a series
of model predictions with different levels of complexity illustrate
the necessity of such a sophisticated structure model for biomass
particle combustion modeling. Finally, more model investigations and experimental data are presented and discussed.
Single-Particle Combustion Model Validation. Combustion
experiments in the single-particle reactor validate the combustion
model by comparisons of particle surface temperature, internal
temperature, and mass loss during drying, devolatilization, and
char oxidation.
The single-particle reactor wall temperature is not uniform
in the axial direction due to reactor configurations, so an average
wall temperature determined at the location of the particle is
(52) Raveendran, K.; Ganesh, A.; Khilart, K. C. Influence of Mineral
Matter on Biomass Pyrolysis Characteristics. Fuel 1995, 74 (12), 1812–
1822.
(53) Merrick, D. Mathematical models of the thermal decomposition
of coal - 2. Specific heats and heats of reaction. Fuel 1983, 62 (5), 540–
546.
(54) Gronli, M. G.; Melaaen, M. C. Mathematical model for wood
pyrolysis - comparison of experimental measurements with model predictions. Energy Fuels 2000, 14, 791–800.
(55) DIPPR. Design Institute of Physical Property Data. http://dippr.byu.edu/index.asp [cited; available from: http://dippr.byu.edu/index.asp.
(56) Lee, C. K.; Chaiken, R. F.; Singer, J. M. Charring pyrolysis of
wood in fires by laser simulation. Symp. (Int.) Combust, 16th, MIT, Aug
15-20 1976, 1459–1470.
(57) Kansa, >E. J.; Perlee, H. E.; Chaiken, R. F. Mathematical model
of wood pyrolysis including internal forced convection; 1977, 29, 3,
311-324.
(58) Patankar, S. V. Numerical Heat Transfer and Fluid Flow. In Series
in Computational Methods in Mechanics and Thermal Sciences; Taylor &
Francis: New York, 1980.
2834 Energy & Fuels, Vol. 22, No. 4, 2008
Lu et al.
Table 4. Physical Properties of Biomass Particles
property
wood density FB
porosity emissivity ω
permeability η (Darcy)
thermal conductivity k (W/(m · K))
biomass particle specific surface area Sa (m2/m3)
char particle specific surface area Sa,char (m2/m3)
pore size dpore (m)
hydraulic pore diameter, dpore,hydraulic
molecular weight M (kg/kmol)
viscosity µ (Pa · s)
diffusivity DAB (m2/s)
value
ref
650 kg/m3 (sawdust), 580 kg/m3 (poplar particle)
0.4
ωA ) 0.7, ωB ) 0.85, ωC ) 0.95
ηB ) 1, ηC ) 100
kj, gas species thermal conductivity is calculated based on DIPPR correlations
kA ) 1.2
wet biomass in tangential direction:
if Cw > 0.4:
kB ) (9.32 × 10-2 + 6.5 × 10-3Cw)(1 + 3.65 × 10-3(T 273.15))(0.986 + 2.695Cw)
if Cw e 0.4:
kB ) (0.129-4.9 × 10-2Cw)(1 + (2.05 + 4Cw) × 10-3(T 273.15))(0.986 + 2.695Cw)
thermal conductivity in axial direction is 2.5 times of the tangential one
kC ) 0.071
9.04 × 104
1.0 × 106
3.2 × 10-6
dpore,hydraulic ) 4.0ε/Sa(1.0 - ε)
MT ) 145
µgas ) 3 × 10-5 for all gas species
DAB ) 3.0 × 10-5 for all gas species
( )
Deff,bw ) D0 exp
-Eb
RT
54
55
42
56
BET
BET
BET
9
57
9
45
Eb ) a1 - a2Cbw
where Cbw is bound water content, D0 ) 5 × 10-5 m/s, a1 )
31030 J/mol, and a2 ) 10000 J/mol
kfw )
heat capacity Cp (J/(kg · K))
{
Deff,fw ) 6.1 × 103
0,
Φ
kfw
( )
( (
( ) ( )
43
kfw 0.61 FsCfw
ε
ηfw
Ffw
FsCfw
e Sir
εFfw
π (FsCfw/εFfw) - Sir
1 - cos
,
2
1 - Sir
if
)) ( )
if
FsCfw
> Sir
εFfw
φ ) 3.0 × 10-15 m2
Sir ) 0.1, irreducible saturation, kfw
(
)[ ( ) ( )]
53
)[ ( ) ( )]
where
53
1000Rg
380
1800
g
+ 2g
Cp,B )
7.72
T
T
Cp,C )
(
1000Rg
380
1800
g
+ 2g
11.3
T
T
g(x) )
x2ex
(ex - 1)2
Cp,T ) -100 + 4.4 × T - 0.00157 × T2
Cp,j of all gas species except hydrocarbon is based on DIPPR database
correlations
used in the model as the reactor wall temperature. Both a type
K thermocouple and the imaging pyrometer measure this
temperature. The thermocouple reading was 1303 K and the
average pyrometer measurement was 1276 K. The imaging
pyrometer data are taken as the wall temperature here. A type
K thermocouple monitors the center gas temperature. The actual
gas temperature was corrected for radiative and other losses from
the thermocouple bead based on the wall temperature, bulk gas
velocity, and the thermocouple bead size. This resulted in a gas
temperature of 1050 K.
Particle Devolatilization. Data for a near-spherical particle
(dp ) 11 mm) with aspect ratio of 1.0 and a moisture content
of 6.0 wt %, including mass loss, center and surface temperature
during pyrolysis, appear with model predictions in Figures 4
and 5. The nominal conditions of this experiment include a
54
55
reactor wall temperature of 1273 K and gas temperature of 1050
K. All the following validation experiments used the same
conditions.
The particle mass loss and particle surface temperature
predictions generally agree with experimental data except that
the measured particle center temperature increases faster than
the model predictions at the beginning. This discrepancy
likely arises from thermal conduction through the thermocouple wire, as discussed later. In principle, the measured
particle surface temperature and center temperature should
reach the same value at the end of pyrolysis, but a small
discrepancy exists in differences in thermocouple bead size
and shape and ash coating on the center temperature bead.
A more detailed discussion of the features of these data
Biomass Particle Combustion
Figure 4. Temperature of near-spherical particle during pyrolysis in
nitrogen (dp ) 9.5 mm, AR ) 1.0, MC ) 6 wt %, Tw ) 1276 K, Tg )
1050 K).
Figure 5. Mass loss of near-spherical particle during pyrolysis in
nitrogen (dp ) 9.5 mm, AR ) 4.0, MC ) 40 wt %, Tw ) 1276 K, Tg
) 1050 K).
appears after discussion of the potential cause of the
discrepancy in the center temperature data.
To determine the thermocouple lead wire impact on the
measured center temperature, a second experiment at the same
conditions used a cylindrical particle of the same diameter but
with aspect ratio of 4.0. Two thermocouples monitored the
center temperature, one passing axially and a second passing
radially through the particle. The axial thermocouple should be
less impacted by heat conduction through the leads since the
particle provides some insulation from the radiation and
buoyancy-driven bulk-flow convection. In Figure 6, lines 1 and
2 are particle center temperatures measured in the radial
direction; lines 3 and 4 are results measured in axial direction.
As indicated, the center temperature measured in the radial
direction increases much faster than that measured in axial
direction at the beginning, indicating that the thermocouple wire
conduction influences initial center temperature measurements.
The model prediction for the center temperature generally agrees
with the average of the axial direction data.
Mass loss data collected in several runs for the cylindrical
particle appear with model predictions in Figure 7.
The shapes of the temperature histories illustrate the complexity of this large-particle pyrolysis process even in the
absence of complications arising from surface oxidation and
surrounding flames. The initial low center temperature is
associated with vaporization, which occurs at subboiling temperatures under nearly all conditions. Experiments with more
moist particles reported later illustrate more clearly the impacts
of vaporization. After vaporization, particles heat up relatively
Energy & Fuels, Vol. 22, No. 4, 2008 2835
Figure 6. Temperature comparison of a cylindrical particle during
pyrolysis in nitrogen (dp ) 9.5 mm, AR ) 4.0, MC ) 6 wt %, Tw )
1276 K, Tg ) 1050 K).
Figure 7. Mass loss comparison of a cylindrical particle during pyrolysis
in nitrogen (dp ) 9.5 mm, AR ) 4.0, MC ) 6 wt %, Tw ) 1276 K, Tg
) 1050 K).
slowly, mainly because devolatilization reactions in outer layers
of the particle generate significant gas velocities in the pores
(commonly reaching 0.2 m/s), thereby impeding internal heat
transfer. After devolatilization, particle temperature increases
rapidly, mainly because the particle mass is greatly reduced
relative to the early data by virtue of volatile losses but
significantly because the internal heat transfer impediment from
rapid outgassing also subsides. By contrast, the surface particle
temperature increases rapidly and is less susceptible to slow
heat transfer rates or even significant impacts from the blowing
factor, in this case because radiation is the dominant heating
mechanism. If convection were the primary heating mechanism,
surface temperature heating rates would decrease by factors of
up to 10 during rapid mass loss due to the outgassing effects.
These processes result in temperature differences between the
surface and the center of many hundreds of degrees Kelvin
during particle heatup.
Particle Drying and Devolatilization. The drying model was
further tested using wet particles with higher moisture content.
Particle surface temperature and center temperature were
measured with type K thermocouples in a cylinder particle with
40 wt % moisture (based on total wet particle mass) during
drying and devolatilization. Similar to the previous experiments,
particle center temperature measured in both axial and radial
directions produced different results, with those in the axial
direction more reliable. Results appear in Figure 8, which
includes model predictions and data. Lines 1 and 2 indicate the
center temperature measured in the radial direction, and lines 3
and 4 indicate the axial measurement. Both the model prediction
and experimental data showed that the particle temperature first
2836 Energy & Fuels, Vol. 22, No. 4, 2008
Figure 8. Temperature comparisons of a cylindrical particle during
drying and pyrolysis in nitrogen (dp ) 9.5 mm, AR ) 4.0, MC ) 40
wt %, Tw ) 1276 K, Tg ) 1050 K).
rises to a constant value near but below the boiling point, with
evaporation mainly occurring in this stage. Following drying,
the particle temperature increases rapidly until biomass devolatilization slows the particle heating rate due to endothermic
decomposition of biomass materials (minor effect) and the effect
of rapid mass loss on the heat transfer coefficient, often called
the blowing parameter (major effect if convection dominates
the particle heatup). Once all biomass material converts to char,
light gas, and tar, the residual char undergoes a rapid center
temperature rise due to its lower mass (major effect), lower heat
capacity (minor effect) and return of the blowing factor to near
1.
During most of the particle history, the predicted surface
temperature is approximately 200 K below the average measured
surface temperature. The predicted surface temperature depends
primarily on radiative heating, convective heating, the impact
of the blowing factor on heat transfer, and the rate and
thermodynamics of water vaporization. As discussed later, the
blowing factor in this radiation-dominated environment has little
impact on the predictions. The thermodynamics of water
vaporization are in little doubt, although the thermodynamics
of the chemically adsorbed water losses are relatively uncertain.
It is also possible that the reactions of the particle with its
attendant changes in size and composition compromise the
thermal contact between the surface thermocouple and the
particle. There is no clear indication of whether the discrepancy
arises from experimental artifacts or from uncertainties in
emissivity and transport coefficients or other factors.
Figure 9 compares the predicted and measured mass loss data.
The model does not predict the measured trend within its
uncertainty though the predictions and measurements are in
qualitative agreement. The disagreement is likely related to the
temperature issues discussed above, including the nonuniformity
of reactor temperature distribution. For a cylindrical particle
horizontally oriented in the center of the reactor, its ends were
exposed to higher temperature environment but the model
applied an average bulk gas center temperature.
Particle Combustion. Figure 10 shows the temperature
profiles of a wet, near-spherical particle with 40 wt % moisture
content (based on the total wet particle mass) and aspect ratio
of 1.0 during combustion.
A type B thermocouple provides temperature data for
combustion experiments since the peak temperatures exceed the
reliable range of type K thermocouples. The measured particle
surface temperatures are not consistent with model prediction
due to experimental artifacts associated with a shrinking particle.
The surface contact is lost as the particle shrinks, and the bead
Lu et al.
Figure 9. Mass loss of a cylindrical particle during drying and pyrolysis
in nitrogen (dp ) 9.5 mm, AR ) 4.0, MC ) 40 wt %, Tw ) 1276 K,
Tg ) 1050 K).
Figure 10. Temperature profiles of a near-spherical wet particle during
combustion in air (dp ) 9.5 mm, AR ) 1.0, MC ) 40 wt %, Tw )
1276 K, Tg ) 1050 K).
becomes exposed to the surrounding flame. The measured
particle center temperatures appear to disagree with model
predictions, though the disagreement arises primarily from
thermocouple wire conduction. Both experimental data and
model predictions show that during the char burning stage the
particle temperature increases to a peak value and then declines
dramatically. This supports theoretical descriptions of largeparticle combustion mechanisms. Oxidizer diffusion rates
primarily control combustion rates in char consumption, which
proceeds largely with constant density and shrinking particle
diameter. The char particle oxidation front finally reaches the
center of the particle as particle size gets smaller with ash built
up in the outer layer of the particle. The pseudo-steady-state
combustion rate/temperature of the particle first increases then
decreases with size due to changes in the relative importance
of radiation losses, convection, and diffusion. Once the char is
completely consumed, the particle (ash) cools rapidly to near
the convective gas temperature, depending on the radiative
environment.
The corresponding mass loss curves as functions of time
appear in Figure 11. In this case, the data and predictions nearly
overlap, though there remains a slight underprediction of the
mass loss rate. This consistent underprediction could be partially
caused by convective drag on the particle, making it appear
less massive on the scale than it is.
For a low moisture content (6 wt %), near-spherical particle
(dp ) 9.5 mm, AR ) 1.0), the flame temperatures are measured
with both thermocouple and camera pyrometry. A type B
thermocouple mounted near the particle surface provides some
measurements of the flame temperature surrounding the particle.
Biomass Particle Combustion
Figure 11. Mass loss of a near-spherical wet particle during combustion
in air (dp ) 9.5 mm, AR ) 1.0, MC ) 40 wt %, Tw ) 1276 K, Tg )
1050 K).
Energy & Fuels, Vol. 22, No. 4, 2008 2837
Figure 13. Effects of temperature gradients on particle pyrolysis in
nitrogen Nonisothermal assumption for model 1 and isothermal
assumption for model 2 (dp ) 9.5 mm, AR ) 1.0, MC ) 6 wt %, Tw
) 1273 K, Tg ) 1050 K).
Figure 12. Flame temperature comparison during a near-spherical
particle combustion in air (dp ) 9.5 mm, AR ) 1.0, MC ) 6 wt %, Tw
) 1273 K, Tg ) 1050 K).
The upper limit of a type B thermocouple is about 2100 K, and
the thermocouple data above this value are not accurate, as
shown in Figure 12. The flame temperature was also interpreted
by the imaging pyrometer with gray-body emission assumption,
where the results are combinations of flame and particle surface
radiations. Both thermocouple and pyrometry data are compared
with model predictions in Figure 12, where the flame receded
away from the thermocouple after devolatilization. The thermocouple measurements fluctuate due to the turbulence and twodimensional effects caused by the bulk gas convection, which
is not captured in this one-dimensional model. In the camera
pyrometry measurements, soot was assumed as gray-body
emitter, although there is some spectral character to soot
emission and the camera pyrometry measurements can be
improved if spectral-dependent emissivity is applied in the
calculation.59 The model prediction of the flame indicates the
transition of combustion from devolatilization stage to char
burning stage, appearing in Figure 12. Results show that model
predictions generally agree with both the camera-measured data
and thermocouple data, and the difference is within measurements uncertainty.
This now-validated particle combustion model predicts the
relative importance of effects of different factors such as
temperature gradients, blowing, and flame reaction, as illustrated
below.
Nonisothermal Effects. Both experimental data and model
predictions showed that large temperature gradients exist in large
biomass particles during combustion. An isothermal particle
assumption incorrectly predicts both temperature and mass loss
(59) Murphy, J. J.; Shaddix, C. R. Influence of scattering and probevolume heterogeneity on soot measurements using optical pyrometry.
Combust. Flame 2005, 143 (1-2), 1–10.
Figure 14. Blowing factor during particle pyrolysis process in nitrogen
(dp ) 9.5 mm, AR ) 1.0, MC ) 6 wt %, Tw ) 1273 K, Tg ) 1050 K).
for large particles, as illustrated in Figure 13, where pyrolysis
experimental data of a 9.5 mm dry, near-spherical particle are
compared with model predictions with isothermal and nonisothermal assumptions. The model with isothermal assumptions
predicts overall conversion rates approximately three times faster
than the nonisothermal model, the latter being in good agreement
with experimental data. In the isothermal prediction, the surface
temperature, which controls the rate of convective and radiative
heat transfer, is the same as the average particle temperature.
The prediction with the temperature gradient indicates the
surface temperature increases much faster than the average
temperature, decreasing the average driving force for heat
transfer and prolonging the reaction time of the particle. The
difference between isothermal predictions and predictions with
temperature gradients decreases with decreasing particle size,
but the predicted conversion times do not become comparable
(within 10%) until the size is less than 100 µm, which is much
smaller than the average particle size used in commercial
operation.
Effects of Blowing on Particle Temperature. During pyrolysis, the blowing factor of the 9.5 mm particle becomes as low
as 0.1, as shown in Figure 14. This pronounced impact on heat
transfer is not observed when radiation dominates particle
heating, as illustrated by the predicted temperature profiles of
a biomass particle in the single-particle reactor with and without
blowing factor correction in Figure 15, where the particle heating
history is nearly independent of the blowing effects correction.
However, for environments dominated by convective heating,
2838 Energy & Fuels, Vol. 22, No. 4, 2008
Figure 15. Particle temperature profile during particle pyrolysis in
nitrogen with and without blowing factor correction when radiation
dominates (model 1 with blowing factor correction and model 2 without
blow factor correction; dp ) 9.5 mm, AR ) 1.0, MC ) 6 wt %, Tw )
1303 K, Tg ) 1050 K).
Figure 16. Effects of blowing factor on particle temperature during
pyrolysis in nitrogen when convection dominates (Model-1 with
blowing factor correction and model-2 without blow factor correction;
dp ) 9.5 mm, AR ) 1.0, MC ) 6 wt %, Tw ) 298 K, Tg ) 1400 K).
the blowing factor has a major impact on overall heat transfer
rates, and the blowing factor slows down the particle pyrolysis
process by about 20%, as indicated in Figure 16.
Effects of Surrounding Flame during Particle Combustion. The current single-particle combustion model simulates
the boundary layer and the flame formed around the particle
surface in the boundary layer, as well as predicting the boundary
layer thickness.
Figure 17 illustrates the effects of the boundary layer
simulation and surrounding flame on the particle temperature
profiles during combustion. Simulations both including and
neglecting the surrounding flame appear in this graph. As
expected, essentially no difference exists between the two
simulations early in devolatilization (flame not yet ignited).
Slight differences in the surface temperature start to appear
during the late devolatilization stage and early oxidation stage
of combustion, but the flame actually decreases the predicted
surface temperature in this case. This counterintuitive decrease
is associated with the flame consuming oxygen in the boundary
layer that otherwise would have reacted with the particle. The
relatively minor thermal feedback from the flame to the particle
impacts the particle surface temperature less than the reduction
in surface reaction associated with the decreased oxygen
concentration. During the bulk of oxidation, the flame increases
the predicted surface temperature by about 100 K. The modeled
particle final temperatures differ from each other by about 20
K. This minor discrepancy arises from the method applied to
Lu et al.
Figure 17. Effects of flame on near-spherical particle temperature during
combustion in air (model 1 stands for results without flame included,
model 2 for those with flame included; dp ) 9.5 mm, AR ) 1.0, MC
) 6 wt %, Tw ) 1273 K, Tg ) 1050 K).
Figure 18. Particle radius, boundary layer thickness, and off-gas
velocity during a wet particle combustion process in air (dp ) 9.5 mm,
AR ) 1.0, MC ) 6 wt %, Tw ) 1273 K, Tg ) 1050 K).
determine the boundary layer thickness. In the model including
flame layer the boundary layer thickness is based on the linear
heat and mass transfer correlations which were used in the model
without flame layer. In the boundary layer, temperature distribution is not linear for a spherical coordinate and the tangent
(slope) on the surface becomes greater than linear distribution.
This increases the convection heat transfer in the boundary and
hence decreases the particle surface temperature.
Model results also indicate that particle temperature becomes
dramatically more uniform during char burning, although the
flame feedback maintains a surface temperature greater than the
center temperature, unlike theoretical predictions for particles
with oxygen penetration but no flame feedback. These relatively
subtle effects on flame temperatures are too small for accurate
measurements by our techniques.
Generally speaking, nonisothermal effects will slow down
the heat transfer (both radiation and convection) between the
bulk gas and particle surface due to the decrease of temperature
difference. Also for convection-dominated particle heat transfer,
the blowing factor (which is caused by high mass transfer in
the boundary layer) will dramatically reduce the heating rate to
the particle. Surrounding flame affects the particle temperature
mainly during the char burning stage.
The modeled particle radius, boundary layer thickness, and
off-gas velocity as functions of residence time during drying,
devolatilization, and char burning appear in Figure 18.
Although the three processes of drying, devolatilization, and
char oxidation occur simultaneously for large particles such as
the 11 mm poplar particle used in this investigation, they can
Biomass Particle Combustion
still be approximately identified from both experimental data
and model predictions, as shown in Figures 10 and 18. Drying
mainly finishes in the first 20 s followed by primary devolatilization that lasts about 30 s; char oxidation requires an additional
30 s. The modeling results also show that the particle shrinks
slightly during drying and shrinks more rapidly during char
burning.
The comparisons between experimental data and model
predictions with different levels of complexity demonstrate that
for biomass particle combustion a model with such a sophisticated structure is necessary, which takes particle shape, size,
surface area, temperature and concentration gradients, and flame
effects into account.
5. Conclusions
A relatively general purpose particle combustion model
capable of simulating drying, recondensation, devolatilization,
and char oxidation and gasification, and swelling/shrinking as
well as gas-phase combustion surrounding biomass particles was
developed to compare with original data. Comparisons were
made of particle center and surface temperatures and overall
mass loss. Model predictions included many additional features
of biomass combustion less amenable to direct measurement.
The data and model developed in this investigation describe
single-particle biomass combustion rates reasonably well.
Generally, agreement within a few percent of the measured
values is achieved, though in most cases there remain generally
small but statistically signficant differences between predictions
and measurements.
Isothermal spherical mathematical approximations for fuels
that either originate in or form aspherical shapes during
combustion poorly represent combustion behavior when particle
size exceeds a few hundred microns. This includes a large
fraction of the particles in both biomass and black liquor
combustion. In particular, composition and temperature gradients
in particles strongly influence the predicted and measured rates
of temperature rise and combustion, with large particles reacting
more slowly than is predicted from isothermal models.
Acknowledgment. This investigation is supported by US
Department of Energy (DOE)/EE Office of Industrial Technologies.
Thanks are given to Drs. Thomas Fletcher, Søren Kær, and Dale
Tree for helpful discussions. Justin Scott, Paul Foster, Kelly Echoes,
Brian Spears, and Russ Johnson contributed to this project.
Nomenclature
A ) pre-exponential factor, s-1; area, m2
AR ) aspect ratio
BLT ) boundary layer thickness, m
Cp ) heat capacity, J · kg-1 · K-1
d ) diameter, m
Deff ) effective diffusivity, m2 · s-1
DAB ) molecular diffusivity, m2 · s-1
DK ) Knudson diffusivity, m2 · s-1
Energy & Fuels, Vol. 22, No. 4, 2008 2839
Ei ) activation energy, J · mol-1
hf ) heat transfer coefficient, W · m-1 · K-1
hm ) mass transfer coefficient, m · s-1
Ĥ ) enthalpy, J · kg-1
k ) rate constant; devolatilization reaction ) s-1; heterogeneous
reaction ) m · s-1
K ) thermal conductivity, W/m · s
M ) molecular weight, kg · kmol-1
MW ) gas average molecular weight, kg · kmol-1
n ) shape factor
Nu ) Nusselt number
p ) pressure, Pa
Pr ) Prandtl number
r ) radius coordinate, m; reaction rate, kg · m-3 · s-1
Re ) Reynolds number
R/Rg ) universal gas constant, J · mol-1 · K-1
Rp ) particle radius, m
RSA ) surface area ratio
t ) time, s
Sa ) particle specific surface area, m2 · m-3
SA ) surface area, m2
T ) temperature, K
u ) gas velocity, m · s-1
V ) volume, m3
x ) conversion
Y ) mass fraction
Greek symbols
R ) proportional factor
β ) particle/droplet swelling/shrinking factor
) porosity
µ ) viscosity, Pa · s
η ) permeability, Darcy
θ ) blowing factor
F ) density, kg · m-3
∆H ) heat of reaction, J · kg-1
Subscripts
0 ) initial value or reference state
A ) ash
B ) biomass
C ) char
con ) conductivity
eq ) equivalent
G ) gas phase
G ) light gas
HC ) hydrocarbon
I ) species or component in solid phase
J ) species or component in gas phase
K ) species or component in liquid phase
I ) inert gas
M ) moisture
P ) particle
rad ) radiation
V ) water vapor
T ) tar
w ) wall
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